# A NOTE ON DECOMPOSITION OF COMPLETE EQUIPARTITE GRAPHS INTO GREGARIOUS 6-CYCLES

• Cho, Jung-Rae (DEPARTMENT OF MATHEMATICS PUSAN NATIONAL UNIVERSITY)
• Published : 2007.11.30
• 82 3

#### Abstract

In [8], it is shown that the complete multipartite graph $K_{n(2t)}$ having n partite sets of size 2t, where $n{\geq}6\;and\;t{\geq}1$, has a decomposition into gregarious 6-cycles if $n{\equiv}0,1,3$ or 4 (mod 6). Here, a cycle is called gregarious if it has at most one vertex from any particular partite set. In this paper, when $n{\equiv}0$ or 3 (mod 6), another method using difference set is presented. Furthermore, when $n{\equiv}0$ (mod 6), the decomposition obtained in this paper is ${\infty}-circular$, in the sense that it is invariant under the mapping which keeps the partite set which is indexed by ${\infty}$ fixed and permutes the remaining partite sets cyclically.

#### Keywords

multipartite graph;graph decomposition;gregarious cycle;difference set

#### References

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#### Cited by

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2. Some gregarious kite decompositions of complete equipartite graphs vol.313, pp.5, 2013, https://doi.org/10.1016/j.disc.2012.10.017
3. ON DECOMPOSITIONS OF THE COMPLETE EQUIPARTITE GRAPHS Kkm(2t)INTO GREGARIOUS m-CYCLES vol.29, pp.3, 2013, https://doi.org/10.7858/eamj.2013.024